Flexible and inexact Krylov methods for inverse problems #

Malena Sabaté Landman

10:30 Tuesday in 2Q48.

Part of the Advances in applied numerical linear algebra and its applications session.

Abstract #

Krylov methods are a powerful family of iterative solvers for linear systems, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited to large-scale problems, as they only require matrix-vector products with the system matrix (and its adjoint) to compute approximate solutions, and they display a very fast convergence.

In this talk I will give a general overview on flexible and inexact Krylov methods, which are slowly paving their way towards modern real-life applications that involve more complex and specific needs (e.g. the use of particular matrix structures or the need for specific regularization). After highlighting some examples (CT applications, blind deblurring, …) I will also draw attention towards some of the challenges that this algorithms still need to overcome.